DSPA Chapter 5 Dimensionality Reduction

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Dimensionality reduction techniques enable exploratory data analyses
by reducing the complexity of the dataset, still approximately
preserving important properties, such as retaining the distances between
cases or subjects. If we are able to reduce the complexity down to a
few dimensions, we can then plot the data and untangle its intrinsic
characteristics.

We will (1) start with a synthetic example demonstrating the
reduction of a 2D data into 1D, (2) explain the notion of rotation
matrices, (3) show examples of principal component analysis (PCA),
singular value decomposition (SVD), independent component analysis (ICA)
and factor analysis (FA), and (4) present a Parkinson’s disease
case-study at the end.